Question: Luis is 24 years older than William. For the last two years, Luis and William have been going to the same school. Six years ago, Luis was 4 times as old as William. How old is Luis now?
Answer: We can use the given information to write down two equations that describe the ages of Luis and William. Let Luis's current age be $l$ and William's current age be $w$ The information in the first sentence can be expressed in the following equation: $l = w + 24$ Six years ago, Luis was $l - 6$ years old, and William was $w - 6$ years old. The information in the second sentence can be expressed in the following equation: $l - 6 = 4(w - 6)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $l$ , it might be easiest to solve our first equation for $w$ and substitute it into our second equation. Solving our first equation for $w$ , we get: $w = l - 24$ . Substituting this into our second equation, we get the equation: $l - 6 = 4($ $(l - 24)$ $ -$ $ 6)$ which combines the information about $l$ from both of our original equations. Simplifying the right side of this equation, we get: $l - 6 = 4l - 120$ Solving for $l$ , we get: $3 l = 114$ $l = 38$.